Derivative of integral / Integral of derivative, but cannot use integration by parts
From the fundamental theorem of calculus, $\int_a^b \frac{d}{dx}f(x)=f(b)-f(a)$ , provided that $\frac{d}{dx}(f(x))$ is continuous. In your case, your function is a product of infinitely many times differentiable functions, so you can apply the theorem and deduce the value of the integral by substituting the endpoints into the function.